87944 ÷ 7 = 12563 R3
Alright, let's work through the division of 87944 by 7 step by step.

Step 1:
7 goes into 8 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 7 from 8 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 7

Step 2:
7 goes into 17 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 12
Subtract 14 from 17 to get 3.
Bring next digit (9) of the dividend behind the 3 and repeat the process: 39 / 7

Step 3:
7 goes into 39 5 times with a remainder of 4.
Write down 5 as next digit of of the result. 
Result so far: 125
Subtract 35 from 39 to get 4.
Bring next digit (4) of the dividend behind the 4 and repeat the process: 44 / 7

Step 4:
7 goes into 44 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 1256
Subtract 42 from 44 to get 2.
Bring next digit (4) of the dividend behind the 2 and repeat the process: 24 / 7

Step 5:
7 goes into 24 3 times with a remainder of 3.
Write down 3 as next digit of of the result. 
Result so far: 12563
Subtract 21 from 24 to get 3.

The final result is 12563 with a remainder of 3.